6,550 research outputs found
The Abel, Fourier and Radon transforms on symmetric spaces
In this paper we prove a new inversion theorem and a refinement of an old
support theorem for two Radon transforms on a symmetric space. Included are
some new identities for the Abel transform and some results about the Fourier
transform from a joint work with Rawat, Sengupta and Sitaram.Comment: 24 page
Spherical Functions on Riemannian Symmetric Spaces
This paper deals with some simple results about spherical functions of type
, namely new integral formulas, new results about behavior at infinity
and some facts about the related functions.Comment: 15 page
The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces
We prove a Paley-Wiener Theorem for a class of symmetric spaces of the
compact type, in which all root multiplicities are even. This theorem
characterizes functions of small support in terms of holomorphic extendability
and exponential type of their (discrete) Fourier transforms. We also provide
three independent new proofs of the strong Huygens' principle for a suitable
constant shift of the wave equation on odd-dimensional spaces from our class.Comment: 26 pages, 1 figur
AKARI near-infrared background fluctuations arise from normal galaxy populations
We show that measurements of the fluctuations in the near-infrared background
(NIRB) from the AKARI satellite can be explained by faint galaxy populations at
low redshifts. We demonstrate this using reconstructed images from deep galaxy
catalogs (HUGS/S-CANDELS) and two independent galaxy population models. In all
cases, we find that the NIRB fluctuations measured by AKARI are consistent with
faint galaxies and there is no need for a contribution from unknown
populations. We find no evidence for a steep Rayleigh-Jeans spectrum for the
underlying sources as previously reported. The apparent Rayleigh-Jeans spectrum
at large angular scales is likely a consequence of galaxies being removed
systematically to deeper levels in the longer wavelength channels.Comment: Submitted to MNRAS Letter
Shintani functions, real spherical manifolds, and symmetry breaking operators
For a pair of reductive groups , we prove a geometric criterion
for the space of Shintani functions to be finite-dimensional
in the Archimedean case.
This criterion leads us to a complete classification of the symmetric pairs
having finite-dimensional Shintani spaces.
A geometric criterion for uniform boundedness of is
also obtained.
Furthermore, we prove that symmetry breaking operators of the restriction of
smooth admissible representations yield Shintani functions of moderate growth,
of which the dimension is determined for .Comment: to appear in Progress in Mathematics, Birkhause
Wave and Klein-Gordon equations on hyperbolic spaces
We consider the Klein--Gordon equation associated with the Laplace--Beltrami
operator on real hyperbolic spaces of dimension ; as
has a spectral gap, the wave equation is a particular case of our
study. After a careful kernel analysis, we obtain dispersive and Strichartz
estimates for a large family of admissible couples. As an application, we prove
global well--posedness results for the corresponding semilinear equation with
low regularity data.Comment: 50 pages, 30 figures. arXiv admin note: text overlap with
arXiv:1010.237
Can (Electric-Magnetic) Duality Be Gauged?
There exists a formulation of the Maxwell theory in terms of two vector
potentials, one electric and one magnetic. The action is then manifestly
invariant under electric-magnetic duality transformations, which are rotations
in the two-dimensional internal space of the two potentials, and local. We ask
the question: can duality be gauged? The only known and battled-tested method
of accomplishing the gauging is the Noether procedure. In its decanted form, it
amounts to turn on the coupling by deforming the abelian gauge group of the
free theory, out of whose curvatures the action is built, into a non-abelian
group which becomes the gauge group of the resulting theory. In this article,
we show that the method cannot be successfully implemented for
electric-magnetic duality. We thus conclude that, unless a radically new idea
is introduced, electric-magnetic duality cannot be gauged. The implication of
this result for supergravity is briefly discussed.Comment: Some minor typos correcte
Can the Near-IR Fluctuations Arise from Known Galaxy Populations?
Spatial Fluctuations in the Cosmic Infrared Background have now been measured
out to sub-degree scales showing a strong clustering signal from unresolved
sources. We attempt to explain these measurement by considering faint galaxy
populations at z<6 as the underlying sources for this signal using 233 measured
UV, optical and NIR luminosity functions (LF) from a variety of surveys
covering a wide range of redshifts. We populate the lightcone and calculate the
total emission redshifted into the near-IR bands in the observer frame and
recover the observed optical and near-IR galaxy counts to a good accuracy.
Using a halo model for the clustering of galaxies with an underlying LCDM
density field, we find that fluctuations from known galaxy populations are
unable to account for the large scale CIB clustering signal seen by HST/NICMOS,
Spitzer/IRAC and AKARI/IRC and continue to diverge out to larger angular
scales. Our purely empirical reconstruction shows that known galaxy populations
are not responsible for the bulk of the fluctuation signal seen in the
measurements and suggests an unknown population of very faint and highly
clustered sources dominating the signal.Comment: 3 pages, 2 figures. To appear in proceedings of First Stars IV
meeting (Kyoto, Japan; 2012
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